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Help in creating E R Diagram

Dear Members I was trying to create an E R Diagram for question given below, now I am struck in middle. If someone can tell me how to proceed further I will be very thankful to him.

A project handling organization has persons identified by PER – ID and a
LAST – NAME. Persons are assigned to departments identified by DEP – NAME. Persons work on projects and each project has a PROJ – ID and a PROJ – BUDGET. Each project is managed by one department and a department may manage many projects. But a person may work on only some (or none) of the projects in his or her departments. Identify the entities and relationship for this organization and construct an E – R diagram

I have Identified the-
1- Entities--- Persons, Departments, Project
2- Atributes of Entities-- Persons( Id Number and Last Name), Departments( Depart_Name), Project (Project_Id, Project_Budjet)
3-- Relationship-- Person to Department is Many to One because many Persons work in a Department. Project to Department is also Many to one because many projects can be managed by a Department. Person to Project is one to many.

Have I identified the Entities and Relations right If not please tell where?